# What is the Difference Between Ridge and Lasso Regression?

Ridge regression and Lasso regression are both regularization techniques used in linear regression to mitigate issues like multicollinearity and overfitting. They are designed to prevent the model from becoming too complex by adding a penalty term to the regression equation. While they share similarities, they differ in how they apply this penalty and their effects on the model’s coefficients.

## Ridge Regression:

• Ridge regression adds a penalty term proportional to the sum of the squared magnitudes of the coefficients (L2 norm) to the linear regression’s loss function.
• The penalty term forces the model to keep the coefficients small. It doesn’t drive coefficients to exactly zero but rather shrinks them towards zero.
• Ridge regression is effective when you have multicollinearity in the data, where predictor variables are highly correlated. It helps to stabilize the model and reduce the impact of collinearity.
• Ridge regression’s main advantage is that it can handle situations where all features are relevant, and it won’t eliminate any features entirely.

## Lasso Regression:

• Lasso regression also adds a penalty term, but it uses the sum of the absolute magnitudes of the coefficients (L1 norm) in the loss function.
• Lasso has a feature selection property: it can drive some coefficients exactly to zero, effectively excluding certain features from the model.
• Lasso is particularly useful when you suspect that many features are irrelevant or redundant, as it helps in feature selection by automatically setting some coefficients to zero.
• However, Lasso might not perform well in cases of severe multicollinearity since it tends to arbitrarily select one of the correlated features and zero out the others.

## Key differences between Ridge and Lasso Regression:

Below are a few key differences between ridge and lasso regression:

### 1. Penalty Type:

• Ridge uses the L2 norm penalty, which results in all coefficients being shrunk towards zero without necessarily being set exactly to zero.
• Lasso uses the L1 norm penalty, which can drive some coefficients exactly to zero, leading to feature selection.

### 2. Feature Selection:

• Ridge does not perform feature selection. It keeps all features in the model but reduces their impact.
• Lasso can perform feature selection by setting some coefficients to exactly zero, effectively excluding those features from the model.

### 3. Solution Stability:

• Ridge is more stable when multicollinearity is present since it distributes the impact among correlated features.
• Lasso might be less stable when multicollinearity is severe due to its tendency to choose one feature arbitrarily.

In summary, the choice between Ridge and Lasso regression depends on the specific characteristics of your dataset and the goals of your analysis. If multicollinearity is a concern and you believe all features are relevant, Ridge regression might be more suitable. If you suspect that some features are irrelevant and you want automatic feature selection, Lasso regression could be a better choice. Additionally, a combination of both techniques, known as Elastic Net regression, can offer a compromise between the two.

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